The 1-(3-hydroxy-propyl)-1,4-diazepane group is a component of various medicinally active materials. Therefore, 1-(3-hydroxy-propyl)-1,4-diazepane also serves as starting material for the synthesis of such medicinally active materials (see for example German OS No. 2355420). The customary process for production of 1-(3-hydroxy-propyl)-1,4-diazepane consists in the reaction of 1,4-diazepane (homopiperazine) with allyl alcohol or 3-chloropropanol. Hereby the yields are low and for example amount of 34% or 46%. Besides the isolation of the reaction product is cumbersome and expensive. The greatest disadvantage however, in this process is that there is used as starting material 1,4-diazepane. There are numerous processes for the production of this material, which processes, however, likewise only result in low yields. The best synthesis at present consists of the reaction of ethylenediamine with acrylonitrile and subsequent hydrogenation in the presence of Raney-nickel of the N-(2-cyano-ethyl)-ethylenediamine obtained, (see F. Poppelsdorf and R. C. Mayerly, J. Org. Chem. 26 (1961) page 131). The total yield of 1-(3-hydroxy-propyl)-1,4-diazepane based on N-(2-cyano-ethyl)-ethylenediamine, however, also is only 15% with this process. Furthermore, in this process there must be employed four times the molar amount of ethylenediamine per 1 mole of acrylonitrile in order to suppress the addition of a second molecule of acrylonitrile on the reaction product. The separation of the excess ethylenediamine furthermore is difficult and expensive.